PROJECT SUMMARY Studies are proposed to dissect one of the fundamental, binary development decisions that most metazoans make: their sex. The nematode C. elegans determines sex with remarkable precision by tallying X- chromosome number relative to the sets of autosomes (X:A signal): ratios of 1X:2A (0.5) and 2X:3A (0.67) signal male fate, while ratios of 3X:4A (0.75) and 2X:2A (1.0) signal hermaphrodite fate. We have discovered much about the nature and action of the X:A signal and its direct target, a master sex-determination-switch gene that also controls X-chromosome dosage compensation. However, a fundamental question remains: how is the signal interpreted reproducibly in an all or none manner to elicit fertile male or hermaphrodite development, never intersexual development? We pioneer new methods using machine learning neural networks to address this question with single-molecule and single-cell resolution. We also propose to dissect the functional interplay between chromatin modification and chromosome structure in regulating gene expression over vast chromosomal territories. X-chromosome dosage compensation in C. elegans is exemplary for this analysis: we found recently that dosage-compensated X chromosomes have (i) elevated levels of modified histone H4K20me1 compared to autosomes and (ii) a unique three-dimensional architecture. Both are imposed by the dosage compensation complex (DCC). Loss of H4K20me1 disrupts 3D architecture and elevates X gene expression. In the nematode DCC, one subunit is an H4K20me2 demethylase and five subunits are homologs of condensin subunits, which compact and resolve mitotic and meiotic chromosomes. All DCC subunits are recruited specifically to hermaphrodite X chromosomes by an XX-specific subunit that triggers binding to cis- acting regulatory elements on X (rex) to reduce gene expression by half. The DCC remodels the structure of X into topologically associating domains (TADs) using its highest affinity rex sites to establish domain boundaries. Despite this knowledge, important questions underlying the mechanisms of dosage compensation remain. What DCC subunits recognize the X-enriched motifs in rex sites to bind X directly? How does the DCC regulate RNA polymerase II to repress gene expression? What mechanisms underlie H4K20me1's control of chromosome structure, and how does DCC-mediated higher-order structure affect gene expression? Our findings should have broad implications, because (i) condensin complexes control chromosome structure from bacteria to man, (ii) H4K20me1 is enriched on the inactive X of female mammals, (iii) demethylases are linked to tumor progression, and (iv) the H4K20me2 demethylase modulates nematode growth, metabolism, and entry into the quiescent dauer state. Lastly, we will exploit our unexpected finding that rex sites have diverged across Caenorhabditis species separated by 30 MYR, retaining no functional overlap despite strong conservation of the core DCC machinery. This divergence provides an unusual opportunity to study the path for a concerted co- evolutionary change in hundreds of target sites across X chromosomes and the protein complexes that bind them.